Newton's rings

Newton's rings (also Newton rings, named after Isaac Newton ) are light and dark areas or interference colors produced by interference at the air gap between two reflective, almost parallel surfaces.

Formation of rings

Concentric rings formed in the arrangement described below. A lens having a large curvature radius R of the curved surface to a flat glass plate, between the two boundary surfaces, there is an air gap of varying thickness that is Illuminated to the assembly perpendicular to monochromatic light come from the top, both in reflection and in transmission of concentric light and dark rings around the point of contact of lens and glass plate on. With white light produced colored rings whose intensity decreases with the radius.

The colored pattern on soap bubbles and thin oil layers on water have a similar cause as the Newton rings. In contrast to the Newton rings herein, the interference is not created on a thin air gap, but in a thin layer of transparent material.

Explanation

The rings are formed by the interference on the upper and lower boundary surface of the air wedge. At soap bubbles or oil layers on water in daylight ( even better in direct sunlight) produced colored rings. The color arises because radiation with a wavelength close to the layer thickness " interfering " reinforced or extinguishes. The layer thickness must be larger than half a wavelength of light ( 380 nm to 780 nm). The narrower the light source is, the more rings can be seen.

If monochromatic light reflected from the top of the experimental arrangement, appear by constructive and destructive interference alternating light and dark concentric circles whose centers are located at the contact point of the lens to the glass plate. The dark circles are caused by destructive and the bright rings by constructive interference. It interfere with the light waves reflected at the boundary surface during the transition from the lens in the air with those which are reflected at the boundary surface during the transition from the air into the glass plate. If their relative phase position to 180 °, they cancel each other out, it do dark circles. In mutual gain ( phase angle 0 ° ), however, arise bright rings. With increasing distance from the supporting point (the distance between the lens surface and the glass plate increases), this condition is repeated several times. This results in a plurality of rings which are increasingly close to each other with increasing radius, as the gradient of the change in distance increases due to the spherical shape of the lens.

If white light is irradiated, produced colored rings. The reason for the color is the fact that the condition of interference for different wavelengths is satisfied with different gap thicknesses. In view of the overlaying glass lenses, the reflection is at the ready near surfaces coming. If the condition is satisfied for destructive interference, the light of each color is not reflected. There remains the residual spectrum and generates the complementary color. The spacing of the rings for a particular color is the greater, the greater the wavelength of the color. This means that the sequence of colors on the outside gradually shifts. In addition, the rings of different colors overlap and there are colors by additive color mixing. In the enlarged section can be seen in the interior, wide rings clearly separate red and green stripes. Left to himself, the two colors overlap to a yellow. Very outside they appear separated again, but in reverse order.

Derivation of the equation

The path s, the all light rays to travel through the air is,

Taking into account the phase shift of 180 ° when reflected at the optically denser medium, then:

Is a prerequisite for extinction, that the way is an odd multiple of half the wavelength. That is:

Substituting both formulas are equal, the result is:

Abbreviated:

According to height theorem:

Since D is much smaller than R, is:

So:

In the abbreviated equation used:

Shortened recovery:

Migrated results for the radius of the k-th ring:

Occurrence

• Optical surfaces that touch each other, or are facing, as in uncemented lenses. By forcing open or cementing this can be avoided.
• Lenses, mirrors, blanks and plane-parallel plates, which are placed in Prüfglasformen (quality control)
• With framed in glass slides occur fringing. The Newtonian rings caused by the different thickness of air layer between the glass and slide film. The effect can be avoided by rough surfaces of so-called anti - Newton glass.
• You can see Newton's rings in the air layer between mica surfaces in minerals such as muscovite.

Benefits and use

The effect is used to evaluate the quality of the shape of lenses. The number and symmetry of the rings to be observed when inserting the lens into a form of Reference sometimes serves as a measure of the quality. On the basis of the Rings or " contour lines " can also thickness variations of thin films can be estimated. For the non-contact quality inspection of mirrors top and high quality, especially for reflecting telescopes, the effect is utilized.

An early form of the reflex sight was also based on this effect.